In recent years, the development and widespread use of techniques related to computing machines and networks has been increasing the importance in data (personal data) related to the attribute and the behavior of individuals and confidential data of organizations such as corporations. The utilization of the personal data and the confidential data using computation and analysis allows unprecedented new finding to be obtained or a new function to be implemented. Meanwhile, the risk in which the privacy of the individual or the secret of the organization is invaded is regarded as a problem. Therefore, an attention is focused on concealment techniques that allow the personal data or the confidential data to be utilized while being protected. Among the concealment techniques, a homomorphic encryption technique is a concealment technique using an encryption technique. The homomorphic encryption technique is one of public key encryption methods in which a pair of different keys is used in the encryption and in the decryption, and is capable of operating data while the data remains encrypted.
Generally, the homomorphic encryption method conducts an operation corresponding to addition, multiplication, or the like on two or more target ciphertexts without decrypting the ciphertexts, and thus is capable of obtaining ciphertexts that are computation results by conducting addition, multiplication, or the like on their original plain texts. For example, a fully homomorphic encryption method is proposed in which addition and multiplication may be conducted at any number of times. The fully homomorphic encryption method is capable of implementing an operation, such as exclusive OR, AND, and NOT, thereby allowing computations by all kinds of logic circuits to be implemented. Meanwhile, the fully homomorphic encryption method is not practical in performance at present because of the enormous time for the processing such as encryption and decryption, concealment computation or the enormous size of the ciphertexts. Therefore, a somewhat homomorphic encryption technique is proposed that implements a practical performance by limiting the number of multiplications.
One of the applications of the homomorphic encryption is biometric authentication. The biometric authentication performs authentication that a user is an authentic person using biometric information on the user, has an advantage that the user does not have to store a password compared with password authentication. Meanwhile, the biometric information on a user is unchanged through life, and is not capable of being changed and destroyed. Accordingly, there arises a problem of protection against a leakage of the biometric information. In view of this, it is considered that the homomorphic encryption is used for biometric authentication, thereby allowing the degree of similarity to be derived without using a feature vector of a plain text, and safe authentic person authentication with a low possibility of a theft of the plain text to be implemented.
As examples of conventional techniques, the following are known: International Publication Pamphlet No. 2011/052056; C. Gentry, “Fully Homomorphic encryption using ideal Lattices”, STOC '09 Proceedings of the forty-first annual ACM symposium on Theory of computing, 2009 May 31, pp. 169-178; D. Boneh, E-J. Goh, and K. Nissim, “Evaluating 2-DNF Formulas on Ciphertexts”, Theory of Cryptography, Volume 3378 of the series Lecture Notes in Computer Science, February 2005, pp. 325-341; T. Okamoto, and K. Takashima, “Homomorphic encryption and Signatures from Vector Decomposition”, Pairing 2008, LNCS 5209, Springer-Verlag, September 2008, pp. 57-74; and, T. Hirano, M. Hattori, T. Ito, and N. Matsuda, “Cryptographically-Secure and Efficient Remote Cancelable Biometrics Based on Public-Key Homomorphic encryption”, IWSEC 2013, LNCS 8231, Springer-Verlag, November 2013, pp. 183-200.